Mapping a nonequilibrium phase diagram for collective states of sea urchin embryos

Collective motion in biological systems with polar constituents, such as human crowds and bird flocks, arises from agents that consume energy and break time-reversal symmetry. Here, we explore how adding rotational degrees of freedom at the microscopic level affects nonequilibrium phases.

Using sea urchin embryos as active building blocks, we map a nonequilibrium phase diagram with density as the control parameter. These embryos break chiral and rotational symmetry, leading to collective rotational and translational order. At low densities, we observe gas-like motion, while higher densities result in vortex formation and jamming.

By analyzing embryo trajectories, we reveal a continuous phase transition in collective order and extract spatiotemporal modes that govern system dynamics. This work provides insights into designing bio-inspired active materials using microscopic symmetry breaking to create novel dynamical states.